Non-invertible surface defects in 2+1d QFTs from half spacetime gauging

Abstract

We study duality defects in 2+1d theories with \( {\mathbb{Z}}_N^{(0)}\times {\mathbb{Z}}_N^{(1)} \) global symmetry and trivial mixed ’t Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, we define duality defects for theories that are self-dual under gauging. We calculate the fusion rules involving duality defects and show that they obey a fusion 2-category. We also construct the corresponding symmetry topological field theory, obtained from a four-dimensional BF theory gauging a \( {\mathbb{Z}}_N^{\textrm{EM}} \) electric-magnetic symmetry. Furthermore, we provide explicit examples of such duality defects in U(1) × U(1) gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d \( \mathcal{N} \) = (2, 0) SCFTs of type A_N−1 on various three-manifolds.